1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Integral bounds

  1. Dec 3, 2014 #1
    1. The problem statement, all variables and given/known data
    I am having trouble setting up the bounds on the following two integrals:

    (a) The region E bounded by the paraboloid y=x2+z2 and the plane y=4.
    (b) The region bounded by the cylinder x2+y2=1, z=4, and the paraboloid z=1-x2-y2.

    2. Relevant equations

    3. The attempt at a solution
    I thought for (a) to use 4 < y < x2+z2
    -sqrt(y-z2) < x < sqrt(y-z2)
    -sqrt(y-x2) < z < sqrt(y-x2)
    But these don't seem right.
    I'm not sure where to begin for (b) except that z may be upper bounded by 4?
    Thanks in advance.
  2. jcsd
  3. Dec 3, 2014 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member
    2017 Award

    (a) The conditions you put on y will not give you a bounded region. For simplicity, I suggest you start working with ##r=\sqrt{x^2 + z^2}## instead of x and z.

    (b) As in (a), polar coordinates will serve you well here.
  4. Dec 3, 2014 #3


    User Avatar
    Homework Helper

    For these you want to use cylindrical coordinates. For (a), you should take [itex](x,y,z) = (r \cos \theta, y, r \sin \theta)[/itex]. For (b), you should take [itex](x,y,z) = (r \cos\theta, r \sin \theta, z)[/itex].
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted